Quasi-Lipschitz equivalence of quasi Ahlfors-David regular sets

Science China Mathematics

Volumn 54, Issue 12, 2011, Pages 2573-2582

  Wang, Qin ^a   Xi, Li Feng ^a  

^a ZHEJIANG WANLI UNIVERSITY   (China)

Author keywords

Ahlfors David regularity; fractal; quasi Lipschitz equivalence

Indexed keywords

EID: 82555187890     PISSN: 16747283     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11425-011-4282-x     Document Type: Article

References (12)

1. Chen X C, Xi L F. Quasi-Lipschitz equivalence on homogeneous uniform Moran sets. Acta Math Sinica (Chin Ser), 2010, 53: 493-500.
2. David G, Semmes S. Fractured Fractals and Broken Dreams: Self-Similar Geometry Through Metric and Measure. Oxford: Oxford University Press, 1997.
3. Falconer K J. Techniques in Fractal Geometry. Chichester: John Wiley & Sons, Ltd., 1997.
4. Falconer K J, Marsh D T. On the Lipschitz equivalence of Cantor sets. Mathematika, 1992, 39: 223-233.
5. Farb B, Mosher L. A rigidity theorem for the solvable Baumslag-Solitar groups. With an appendix by Daryl Cooper. Invent Math, 1998, 131: 419-451.
6. Mattila P, Saaranen P. Ahlfors-David regular sets and bilipschitz maps. Ann Acad Sci Fenn Math, 2009, 34: 487-502.
7. Wen Z Y. Moran sets and Moran classes. Chinese Sci Bull, 2001, 46: 1849-1856.
8. Xi L F. Lipschitz equivalence of self-conformal sets. J London Math Soc, 2004, 70: 369-382.
9. Xi L F. Quasi-Lipschitz equivalence of fractals. Israel J Math, 2007, 160: 1-21.
10. Xi L F, Ruan H J. Lipschitz equivalence of generalized {1, 3, 5,}-{1, 4, 5} self-similar sets. Sci China Ser A, 2007, 50: 1537-1551.
11. Xi L F, Xiong Y. Self-similar sets with initial cubic patterns. C R Math, 2010, 348: 15-20.
12. Xi L F, Xiong Y. Lipschitz equivalence of fractals generated by nested cubes. Math Z, doi: 10. 1007/s00209-011-0916-5.